Scientific Computing - An Introduction using Maple and MATLAB

✍ Scribed by Walter Gander, Martin J. Gander, Felix Kwok (auth.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 926
• Series: Texts in Computational Science and Engineering 11
• Edition: 1
• Category: Library

✦ Synopsis

Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.

✦ Table of Contents

Front Matter....Pages I-XVIII
Why Study Scientific Computing?....Pages 1-8
Finite Precision Arithmetic....Pages 9-60
Linear Systems of Equations....Pages 61-112
Interpolation....Pages 113-179
Nonlinear Equations....Pages 181-259
Least Squares Problems....Pages 261-385
Eigenvalue Problems....Pages 387-486
Differentiation....Pages 487-515
Quadrature....Pages 517-582
Numerical Ordinary Differential Equations....Pages 583-671
Iterative Methods for Linear Systems....Pages 673-815
Optimization....Pages 817-886
Back Matter....Pages 887-914

✦ Subjects

Computational Mathematics and Numerical Analysis; Algorithms; Computational Science and Engineering; Mathematical Software; Numerical Analysis